Question

If pressure amplitude of a sound wave in a medium is tripled and the wavelength is doubled then amplitude of displacement of the particles in the medium becomes $x$ times of initial value. The value of $x$ is

• A. $5$
• B. $3$
• C. $2$
• D. $6$

Answer 1

The correct option is D $6$

We know the relation between maximum value of pressure in the medium and displacement of the particles in the medium is given by,
$P_o=B{A}_{o}k$
where,
$P_o$ is maximum pressure in the medium, $B$ is bulk modulus of medium, $A_o$ is maximum displacement of particles in the medium and $k$ is wave number of sound wave.
$\Rightarrow P_o=\frac{2\pi B{A}_o}{\lambda }$
$\Rightarrow A_o=\frac{P_o\lambda }{2\pi B}$ .............(1)
If pressure amplitude is tripled and wavelength is doubled then,
$\Rightarrow A_o^{{}^{\prime }}=\frac{3P_o\times 2\lambda }{2\pi B}$
$\Rightarrow A_o^{{}^{\prime }}=\frac{6P_o\lambda }{2\pi B}=6A_o$ [from (1)]